RPN, An introduction to Reverse Polish Notation

The RPN Method: An Overview and History

If you're a frequent calculator user, you owe it to yourself to investigate the advantages of RPN. RPN stands for Reverse Polish Notation. Reverse Polish Notation was developed in 1920 by Jan Lukasiewicz as a way to write a mathematical expression without using parentheses and brackets. Hewlett-Packard Co., realizing that Lukasiewicz's method was superior to standard algebraic(1) expressions when using calculators and computers, adapted RPN for its first hand-held scientific calculator, the HP35, in 1972.

Why Use RPN?

• RPN saves time and keystrokes. You never have to account for the parentheses while doing calculations. The process is similar to the way you learned math on paper.

• You can see the intermediary results as you perform your computations rather than just the answer at the end. This is an extremely helpful byproduct. Math teachers are using this feature to improve student understanding of mathematics

• An intermediate result allows the user to check the results and correct errors more easily. It's easier to follow the stream of calculation. The user defines the priority of operators.

• RPN is logical because the user first gives the number and then tells what to do with it.

HP provides full RPN

Hewlett-Packard produces certain models of calculators with RPN because it is an extremely powerful yet simple way to perform computation. The HP 12c financial calculator uses RPN exclusively. HP also recognizes that some customers prefer the traditional algebraic entry mode. This is why some HP calculators operate in both RPN and algebraic mode. For example, the new 12c Platinum financial, 17bII+ financial, 33s scientific, 48gII graphing and 49g+ graphing can be switched between the two modes.

RPN is also consistent in its usage. Most non-RPN scientific calculators are half RPN and half algebraic. For example, to perform addition, you need to enter 2+4 (algebraic), but to perform a sine calculation, you need first to enter the number and then to press the SIN button, which is a RPN method of entering the equation. HP's RPN calculators do not suffer from this idiosyncrasy.

Learning RPN Is Easy

Believe it or not, the process of using RPN is similar to the way you learned math. If you think about it, you have to modify the way you learned math in order to use an algebraic mode calculator.

Here's an example

3+5
---
7+6

Or (3+5) / (7+6) = x

Algebraic method: Add 3+5=8. Write down the answer or store it in memory. Add 7+6=13. Now enter the 8 from the first answer and then divide it by entering the second answer to get x=0.62.

RPN method: Touch 3 then the ENTER key. Touch 5 then the + key. Touch 7, and then ENTER. Touch 6 then the + key. Note that the answer to the second sum is displayed. Now here's the magic part. Touch the divide key and the calculator gives the answer, 0.62.

Algebraic: 13 strokes, not counting the effort to write down or memorize the first answer while you calculated the second answer.

RPN: 9 strokes, and no need to write anything down.

How RPN Calculators Work

RPN keeps a record of calculations by placing them in a stack(2). In the above example, when you pressed ENTER the second time, the answer to the first sum was pushed(3) up in the stack awaiting the next action. After entering the second sum, pressing the divide key looked at the first sum and divided it by the second and popped(4) the answer out of the stack. In other words, RPN performed the calculation in a logical order.

Learning how to use an RPN calculator usually takes just a few minutes and it can save lots of time and effort over the long run. Here is a practical everyday example that uses RPN.

Every HP calculator designed for RPN comes with a manual that guides you through sample problems using RPN. Take a test drive and you will find out why many of HP's customers have been enthusiastic RPN users for more than 30 years.